For the problems of the form (REF ), we experiment with examples from the Suite Sparse Matrix Collection [1]}. The selected matrices \(A\)  are 65 symmetric positive definite matrices with a number of rows in \([10^2, 10^4]\) , and an estimated condition number \(\le 10^{8}\)  (the condition number is estimated via the routine condest in the Matrix R package). The vector \(\mathbf {b}\)  is chosen so that the solution of \(A\mathbf {x}= \mathbf {b}\)  is \(\mathbf {x}^\ast = \mathbf {e}\) , the vector of all ones.
For all problems, the starting vector is \(\mathbf {x}_0 = -10\,\mathbf {e}\) , and the initial stepsize is \(\beta _{0}^{\rm {}} = 1\) . The algorithm stops when \(\Vert \mathbf {g}_k\Vert  \le {\sf tol}\,\Vert \mathbf {g}_0\Vert \)  with \({\sf tol} = 10^{-6}\) , or when \(5\cdot 10^4\)  iterations are reached. The problem nos4 is scaled by the Euclidean norm of the first gradient.
